A cylinder fitted with a frictionless piston contains R-134a at 100 F, 80% quality, at which point the volume is 3 Gal. The external force on the piston is now varied in such a manner that the R-134a slowly expands in a polytropic process to 50 lbf/in.^2, 80 F. Calculate the work and the heat

Question

A cylinder fitted with a frictionless piston contains R-134a at 100 F, 80% quality, at which point the volume is 3 Gal. The external force on the piston is now varied in such a manner that the R-134a slowly expands in a polytropic process to 50 [latex]lbf / in ^{2}[/latex], 80 F. Calculate the work and the heat transfer for this process.

Accepted Answer

C.V. The mass of R-134a. Properties in Table F.10.1

[latex]v _{1}= v _{ f }+ x _{1} v _{ fg }=0.01387+0.8 imes 0.3278=0.2761 ft ^{3} / lbm[/latex]

[latex]u _{1}=108.51+0.8 imes 62.77=158.73 Btu / lbm ; \quad P _{1}=138.926 psia[/latex]

[latex]m = V / v _{1}=3 imes 231 imes 12^{-3} / 0.2761=0.401 / 0.2761=1.4525 lbm[/latex]

State 2: [latex]v _{2}=1.1035 ft ^{3} / lbm ( ext { sup.vap. }) ; u _{2}=171.32 Btu / lbm[/latex]

(linear interpolation is not so accurate as v is more like ~1/P)

Process: [latex]n =\ln \frac{ P _{1}}{ P _{2}} / \ln \frac{ V _{2}}{ V _{1}}=\ln \frac{138.926}{50} / \ln \frac{1.1035}{0.2761}=0.7376[/latex]

[latex]{ }_{1} W _{2}=\int P dV =\frac{ P _{2} V _{2}- P _{1} V _{1}}{1- n }[/latex]

[latex]=\frac{50 imes 1.1035-138.926 imes 0.2761}{1-0.7376} imes 1.4525 imes \frac{144}{778}=17.23 Btu[/latex]

[latex]{ }_{1} Q _{2}= m \left( u _{2}- u _{1} ight)+{ }_{1} W _{2}=1.4525(171.32-158.73)+17.23= 3 5 . 5 ~ B t u[/latex]

Question 3.303E: A cylinder fitted with a frictionless piston contains R-134a...

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